Question: $\dfrac{d}{dx}\left(\sqrt[5]{x^2}\right)=$
Answer: The strategy We can first rewrite the radical as a rational power of $x$. Then, the derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) Rewriting the radical as a rational power $\sqrt[5]{x^2}=x^{^{\frac{2}{5}}}$ Differentiating using the power rule $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{^{\frac{2}{5}}}\right) \\\\ &=\dfrac{2}{5}x^{^{\frac{2}{5}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac25x^{^{-\frac{3}{5}}} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(\sqrt[5]{x^2}\right)=\dfrac25x^{^{-\frac{3}{5}}}$. This can also be written as $\dfrac{2}{5\sqrt[5]{x^3}}$ (all equivalent forms are accepted).